We showed in section II that dispersion e¤ect is highly correlated with the portfolio’s size. However, many constituents in the portfolio can o¤set the dispersion P&L (or amplify it). We ran di¤erent dispersion strategies with sub-baskets of the original portfolio, that is, EuroStoxx 50. The P&L ob-tained is maximized when the components in the sub-basket have the higher negative correlation. However, the P&L are only 3% bigger than we consider the whole EuroStoxx 50.
Part IV
Conclusions and Future Developments
The rapid development of derivatives market has enabled investors to gain exposure to volatility. So instead of just taking directional positions based on predictions of future returns, investor with foresight of volatilities might also make money by engaging in the appropriate volatility product. Variance swap is the most heavily traded among the volatility products. The payo¤
of this contract is the di¤erence between the future realized return variance and the predetermined variance swap rate.
This thesis tries to explore the pro…tability of the dispersion trading strategies. We begin examining the di¤erent methods proposed to price vari-ance swaps. We have developed a model that explains why the dispersion trading arises and what the main drivers are. We have investigate the P&L obtained with the di¤erent strategies proposed in the market. We show that correlation-based dispersion trading produces the bigger P&L. This strategy demonstrates positive mean of return, which is consistent with the fact that the implied volatility is generally higher than the future realized volatility.
This strategy has a potential of su¤ering large loss in bullish market. We show that dispersion trading strategies are not arbitrage strategies. We have computed the distribution of the P&L obtained. We show that the distri-bution of the P&L shows thick tails. This is consistent with the extreme events that appear in a bullish market (for example, the correction in the market of 2005). We proposed a method to choose the optimal weights that produces outperforming of the strategies used in the market. The timing of the strategy is also studied.
As a further it might be interesting to check the seasonality of the return pro…le and design one optimal entry time. Furthermore, the mark to market value of variance should also be studied because for long maturity contract one might prefer to close the position before maturity.
We have studied the dispersion trading in a Equity Index. An interesting exercise could be to implement the strategy in Credit Indices. This approach needs a previous step: the modi…cation of the pricing method proposed by Derman in order to use Credit Options (in both single Credit Default Swaps and Credit Indices).
Figure 1.
P&L Dispersion Trading
-6 -5 -4 -3 -2 -1 0 1 2 3 4
03/01/2005 03/03/2005 03/05/2005 03/07/2005 03/09/2005 03/11/2005 03/01/2006 03/03/2006 03/05/2006 03/07/2006 03/09/2006 03/11/2006
Date
Vanilla Dispersion
Correlation Weighted Scheme 1
Correlation Weighted Scheme 2
Description Figure 1: P&L (in Vega Notional) obtained selling a variance swap on the EuroStoxx 50 and being long on the constituents. Vanilla dispersion gets exposure to the volatility and correlation-weighted dispersion gets exposure to the correlation. The expiry is three months and the Notional is one Euro.
Figure 2.
Description Figure 2: Distribution function obtained for the Vanilla Dispersion Trading on the EuroStoxx 50.
The weight used is wi.
-0.50 0 0.5 1 1.5 2 2.5
2 4 6 8 10 12
Vanilla Dispersion Distribution Function
Figure 3.
Description Figure 3: Distribution function obtained for the Correlation-Weighted Dispersion Trading (Scheme 1) on the EuroStoxx 50. The weight used is
implied i
i implied
index
w ρ σ
× ×σ .
Figure 4.
Description Figure 4: Distribution function obtained for the Correlation-Weighted Dispersion Trading (Scheme 2) on the EuroStoxx 50. The weight used iswi× ρ .
-5 -4 -3 -2 -1 0 1 2 3 4
0 20 40 60 80 100 120 140 160 180 200
CorrelationWeight2 Distribution Function
-6 -5 -4 -3 -2 -1 0 1 2 3 4
0 50 100 150 200 250
CorrelationWeight1 Distribution Function
Figure 5.
AccumulatedProfits
0 200 400 600 800 1000 1200 1400 1600
03/01/2005 03/03/2005 03/05/2005 03/07/2005 03/09/2005 03/11/2005 03/01/2006 03/03/2006 03/05/2006 03/07/2006 03/09/2006 03/11/2006
CorrelationWeighScheme2
CorrelationWeightScheme1
Vanilla Dispersion
Description Figure 5: Accumulated profits (in Euros) from the different strategies implemented. The initial cost assumed in the strategy is zero. We observe that the 2006 correction affected to the P&L but it did not produce a
negative balance in the accumulated gains.
Table 1.
Weight αi Average Return STD of Return Risk-Return
(no annualized) Skew
w i 0.52669 0.83866 0.62085 -0.75189
implied i
i implied
index
w ρ σ
× ×σ 1.2111 1.4948 0.8101 -2.0271
wi× ρ 1.2023 1.3576 0.88561 -2.0149
Description Table 1: Main Statistics of the P&L for the different strategies implemented.
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